In recent years, there has been a significant amount of research related to the development of quantum computers. If such a computer were to be built, it would be able to break existing public-key cryptosystems that are currently used for many purposes. This will seriously affect the privacy and integrity of digital communications, etc. That is why special attention is currently being paid to post-quantum cryptography, the main goal of which is the development of cryptographic systems that are protected from both quantum and classical attacks, and will also be able to interact with existing communication protocols and networks. In view of the significant importance of the practical application of directional encryption algorithms, at the international and state level, special attention was paid to the implementation of the proposed requirements for key encapsulation protocols. Key-establishment algorithms (KEA) form a common secret – the key for a symmetric encryption algorithm. The paper considers two KEA algorithms that use algebraic lattices: one of the finalists of the 3rd round Crystals-Kyber and the Skelya algorithm (DSTU 8961-2019). The Kyber algorithm first performs asymmetric encryption of a 32-byte message, and then generates a shared secret. The Skelya algorithm performs the same actions, but for asymmetric encryption, it uses messages of any length that do not exceed the maximum possible. That is why the last algorithm can be used not only as a KEA algorithm, but also as an asymmetric encryption algorithm. According to the NIST Security level, the Kyber algorithm provides cryptographic 1, 3, and 5 security levels, and the Rock algorithm provides cryptographic 3, 5, and 7 security levels. The cryptographic stability that is ensured for both algorithms is determined by a set of parameters. Thus, the purpose of this work is to review the details of the implementation of each of the mentioned algorithms, to compare the speed of the key generation, encapsulation and decapsulation algorithms for the Kyber and Skelya algorithms in terms of key data lengths, and the encapsulation result and computational complexity of both algorithms.
In recent years, there has been a significant amount of research related to the development of quantum computers. If such a computer were to be built, it would be able to break existing public-key cryptosystems that are currently used for many purposes. This will seriously affect the privacy and integrity of digital communications, etc. That is why special attention is currently being paid to post-quantum cryptography, the main goal of which is the development of cryptographic systems that are protected from both quantum and classical attacks, and will also be able to interact with existing communication protocols and networks. In view of the significant importance of the practical application of directional encryption algorithms, at the international and state level, special attention was paid to the implementation of the proposed requirements for key encapsulation protocols. Key-establishment algorithms (KEA) form a common secret – the key for a symmetric encryption algorithm. The paper considers two KEA algorithms that use algebraic lattices: one of the finalists of the 3rd round Crystals-Kyber and the Skelya algorithm (DSTU 8961-2019). The Kyber algorithm first performs asymmetric encryption of a 32-byte message, and then generates a shared secret. The Skelya algorithm performs the same actions, but for asymmetric encryption, it uses messages of any length that do not exceed the maximum possible. That is why the last algorithm can be used not only as a KEA algorithm, but also as an asymmetric encryption algorithm. According to the NIST Security level, the Kyber algorithm provides cryptographic 1, 3, and 5 security levels, and the Rock algorithm provides cryptographic 3, 5, and 7 security levels. The cryptographic stability that is ensured for both algorithms is determined by a set of parameters. Thus, the purpose of this work is to review the details of the implementation of each of the mentioned algorithms, to compare the speed of the key generation, encapsulation and decapsulation algorithms for the Kyber and Skelya algorithms in terms of key data lengths, and the encapsulation result and computational complexity of both algorithms.
The article provides a comprehensive analysis of modern quantum-resistant cryptographic standards security based on lattice theory, such as DSTU 8961:2019 ("Skelya"), CRYSTALS-Kyber, and CRYSTALS-Dilithium. These standards are becoming increasingly popular for solving various practical tasks due to their resistance to attacks that can be implemented on quantum computers. As quantum computing gradually transitions from the theoretical to the practical realm, there is an urgent need for the development and improvement of security models capable of addressing these new challenges. This article focuses on applying the cryptanalysis model developed in previous works to specific cryptographic standards based on lattices. Special attention is given to refining security estimates by considering the algebraic structure of q-ary lattices, which form the foundation of the cryptographic problems underlying these standards. It was found that when considering the algebraic structure of q-ary lattices, security estimates differ significantly from those obtained using the GSA model. In particular, for the key encapsulation mechanisms of DSTU 8961:2019 and CRYSTALS-Kyber, the difference between the estimates in these two models can range from 20 to 30 bits of security, with the refined estimates indicating that existing attacks are less effective than previously thought. It was also revealed that for NIST Level 1 security, decoding attacks show better performance compared to embedding attacks, whereas for NIST Level 5 security, the effectiveness of decoding attacks decreases significantly, falling behind embedding attacks. Thus, the results highlight the importance of accounting for the algebraic structure of lattices in obtaining more accurate security assessments. This allows for a better understanding of potential threats and the optimization of existing lattice-based cryptographic transformations.
The study of key encapsulation mechanisms on algebraic lattices is one of the important directions in modern post-quantum cryptography, since many mechanisms are already either standardized (ANSI X.9.98, DSTU 8961:2019 "Skelya") or are promising candidates for standardization (CRYSTALS-Kyber, FrodoKEM). The purpose of this work is to compare the security arguments of DSTU 8961:2019 "Skelya", CRYSTALS-Kyber, FrodoKEM key encapsulation mechanisms. The paper provides a comparison of theoretical evidence in the idealized random oracle (ROM) and quantum random oracle (QROM) models, as well as a comparison of specific values of security parameters in the core-SVP model, which is, in fact, a standard for lattice cryptography. Since all three key encapsulation mechanisms are based on different complex problems (NTRU, Module-LWE, LWE), a comparison of complex lattice theory problems and a comparison of their security arguments are additionally given. The strengths and weaknesses of the considered key encapsulation mechanisms are shown, and areas of research that require more detailed attention are highlighted.
The study of key encapsulation mechanisms on structured lattices is one of the important directions in modern post-quantum cryptography, as many mechanisms are either already standardized (DSTU 8961:2019 "Skelya") or are promising candidates for standardization (CRYSTALS-Kyber). Estimating the complexity of lattice reduction for cryptographic schemes is an old problem. Asymptotic estimates differ greatly from experimental values, therefore, a number of heuristic methods were developed to solve practical problems. The coreSVP model is a standard means of assessing the security of cryptographic schemes on lattices. The purpose of the work is to analyze the encapsulation mechanisms of DSTU 8961:2019 "Skelya" and CRYSTALS-Kyber keys in the coreSVP model. The analysis was performed using two popular heuristics – GSA (Geometric Series Assumption) and the Chen-Nguyen simulator. The analysis showed that the Chen-Nguyen simulator gives slightly lower estimates than the GSA heuristic. As a result of the analysis, it was found that 8961:2019 The “Skelya” and CRYSTALS-Kyber in the coreSVP model for classical computers have slightly lower than declared security values, but for quantum computers the key encapsulation mechanisms provide the declared security levels. Note that during the analysis, the accuracy of the GSA heuristics and the Chen-Nguyen simulator were analyzed separately. Examples of parameters for which heuristics do not give sufficiently accurate results are given. The performed analysis does not take into account the algebraic structure of lattices used in 8961:2019 "Skelya" and CRYSTALS-Kyber. The inclusion of an algebraic structure in the analysis is a further direction of work. The use of simulators is a promising direction, however, more accurate simulators that take into account the structuring of LWE and NTRU arrays are needed.
Recent developments in quantum computing have shed light on the shortcomings of the conventional public cryptosystem. Even while Shor's algorithm cannot yet be implemented on quantum computers, it indicates that asymmetric key encryption will not be practicable or secure in the near future. The National Institute of Standards and Technology (NIST) has started looking for a post-quantum encryption algorithm that is resistant to the development of future quantum computers as a response to this security concern. The current focus is on standardizing asymmetric cryptography that should be impenetrable by a quantum computer. This has become increasingly important in recent years. Currently, the process of standardizing asymmetric cryptography is coming very close to being finished. This study evaluated the performance of two post-quantum cryptography (PQC) algorithms, both of which were selected as NIST fourth-round finalists. The research assessed the key generation, encapsulation, and decapsulation operations, providing insights into their efficiency and suitability for real-world applications. Further research and standardization efforts are required to enable secure and efficient post-quantum encryption. When selecting appropriate post-quantum encryption algorithms for specific applications, factors such as security levels, performance requirements, key sizes, and platform compatibility should be taken into account. This paper provides helpful insight for post-quantum cryptography researchers and practitioners, assisting in the decision-making process for selecting appropriate algorithms to protect confidential data in the age of quantum computing.
The emergence of quantum computing poses an existential threat to classical cryptographic systems that form the backbone of contemporary digital security infrastructure. RSA, the most widely deployed public-key cryptosystem, relies on the computational hardness of integer factorization, a problem efficiently solvable by quantum computers using Shor's algorithm. This impending vulnerability has catalyzed the development of post-quantum cryptographic alternatives designed to withstand both classical and quantum attacks. CRYSTALS-Kyber, standardized by NIST as ML-KEM, represents the forefront of latticebased key encapsulation mechanisms, offering quantum resistance through the Module Learning With Errors (MLWE) problem. This paper presents a comprehensive comparative analysis of RSA and Kyber, examining their mathematical foundations, security architectures, operational characteristics, and performance metrics across diverse computational environments. The study investigates the fundamental trade-offs between legacy systems optimized for classical threat models and emerging quantum-resistant algorithms designed for future-proof security. Through detailed analysis of key generation, encryption/encapsulation, decryption/decapsulation operations, and security guarantees, this research establishes the technical rationale behind NIST's selection of Kyber as the primary post-quantum key establishment mechanism. The findings demonstrate that while RSA maintains advantages in key size efficiency, Kyber's superior performance profile, quantum resilience, and robust security foundation position it as the essential successor for securing digital communications in the quantum era. This comprehensive study provides critical insights for organizations transitioning from classical to post-quantum cryptographic infrastructure
In recent years, there has been significant progress in the creation of quantum computers. If scalable quantum computers are implemented in the near future, this will jeopardize the security of the most widely used public key cryptosystems. The most vulnerable are public-key schemes based on factorization, discrete logarithms and elliptic curve cryptography. Currently, the main task is to develop, evaluate, study and standardize asymmetric crypto transformations at the international level, including mechanisms of key encapsulation and directional encryption, resistant to attacks by violators of the post-quantum period. An important feature of the transition and post-quantum period is the usage of new mathematical methods to opposite quantum crypto analysis. The paper considers the main attacks on the mechanisms of key encapsulation and directional encryption, as well as system-wide parameters of the DSTU 8961: 2019 standard, which affect the resistance to attacks and the complexity of transformations. Methods for generating system-wide parameters of 5 and 7 levels of stability – 512 bits of classical and 256 bits of quantum security, as well as the protection of the algorithm from attacks by third-party channels are considered. The dependence of encryption and decryption time on the level of stability is analyzed. The results of calculations of system-wide parameters for stability levels 256/128, 384/192 and 512/256 are presented, as well as recommendations for the selection of system-wide parameters depending on the environment and computing capabilities. Sets of parameters selected and recommended for use in the DSTU 8961: 2019 standard are given. Conclusions are drawn about the possibility of applying the DSTU 8961 standard in the post-quantum period.